soil moisture retrieval.pptx

Soil moisture retrieval

over bare surfaces

using time-series radar

observations and a

lookup table

representation of

forward scattering

Seung-bum Kim, Shaowu Huang*, Leung Tsang*,

Joel Johnson**, Eni Njoku

Jet Propulsion Lab., California Inst. Technology

* Univ. Washington

** The Ohio State Univ.IGARSS 2011, Vancouver, Canada

S.B. Kim - 1 -IGARSS 2011

Objectives

• A ‘bare and sparsely vegetation surface covers 13% of the world’s land surface.

• Over vegetated surfaces, a soil moisture signal comes from the bare surface.

– Accurate soil moisture retrieval over the bare surface forms the basis of global soil moisture

retrieval

• We focus on the soil surface where the roughness has the isotropic random distribution.

• We study the retrieval of soil moisture at L-band at 40deg incidence angle to apply to the Soil Moisture

Active Passive (SMAP) mission

• NASA’s SMAP mission

– Global, high-resolution mapping of soil moisture

(top 5cm) and its freeze/thaw state

– Three year mission, due for launch in 2015

– 1000 km-wide swath, enabling 2−3 day revisit

– Retrievals with radiometer (36km resolution), SAR

(3km), and SAR/radiometer combined (9km)

– Multi-pol (HH, VV, HV)

– To achieve the global coverage, the number of

single looks was compromised (60, worst case),

leading to somewhat large speckle. Total radar

measurement error ranges from 0.5dB (13%) to

0.7dB (17%)


Issues with bare surface soil moisture retrieval

• Four parameters dominating the radar scattering from bare surface: surface roughness (s), soil moisture

(Mv), correlation length of roughness (l), correlation function (F)

• Issues to resolve for accurate soil moisture retrieval

– With HH, VV, HV, we cannot determine all 4 unknowns

– Knowledge of correlation length and function is very inaccurate (50% error).

– Ambiguity: dry & rough soil σ0 ~ wet & smooth soil simga0 can lead to multiple solutions

– 13% to 17% radar measurement error

• Past literature

– Empirical retrieval model without considering l or F (Oh et

al. 1992; Dubois et al. 1995)

– The exponential function fits data well (Shi et al. 1997;

Mattia et al. 1997)

– Estimate s and l after assuming temporally static

• Using ancillary dry condition (Rahman et al. 2008)

• Using one time measurement (Joseph 2008)

• Statistical estimate (Verhoest et al. 2007)

• Using ancillary weather model (Mattia et al. 2009)

– Eliminate s during retrieval (Shi et al. 1997)

• Our goal: develop non-empirical and simple method that does

not need ancillary information


Soil moisture retrieval method

• A forward model (Numerical Maxwell Model in 3-Dimension, NMM3D, Huang et al. 2010; 2011)

is inverted using its lookup table representation.

– The NMM3D computes numerical solutions of Maxwell’s equations without approximate

parameterizations or tuning.

– The NMM3D predictions compare well with in situ datasets representing wide ranges of

roughness, soil moisture, and correlation length.

Results with correlation length/rms height (l/s) =4,7,10 is also available.

rmse=1.49dB (VV)

1.64dB (HH)

Huang, Tsang,

Njoku, Chen,

TGRS, 2010


Parameterized IEM based

on 3 Mv and 3 ks simulations

RMS Error = 0.0067 cm3/cm3

Lookup table

RMS Error = 0.0016 cm3/cm3

Courtesy: J.J. van Zyl

10log

shh

= -20.17 +15.33mv+13.63log ks( )

10log

svv

= -18.81+ 25.33mv+10.99log ks( )

• The retrieval based on a lookup table performs better. In comparison, the inversion of a sophisticated model (IEM) is not as accurate.

Retrieval with a lookup table


Soil moisture retrieval method

• Two-polarization (HH and VV) are used for input.

HV channel is set aside for vegetation information

for future. Mv and roughness are retrieved.

• 2N independent input (HH and VV, N is the

number of time-series)

– N+1 unknowns assuming roughness does

not change in time.

• The retrieval of the soil moisture is accomplished

by the least square minimization.

• Time-invariant roughness is estimated first.

• Then time-varying soil moisture is retrieved.

C s,er1,er2 ,..,erN( ) = w1,HH sHH

0 t1( ) - s HH ,LUT

0 s,er1( )( )2

+ w1,VV sVV

0 t1( ) - sVV ,LUT

0 s,er1( )( )2

+w2,HH s HH

0 t2( ) - sHH ,LUT

0 s,er2( )( )2

+ w2,VV sVV

0 t2( ) - sVV ,LUT

0 s,er2( )( )2

+...

+wN ,HH s HH

0 tN( ) - s HH ,LUT

0 s,erN( )( )2

+ w1,VV sVV

0 tN( ) - sVV ,LUT

0 s,erN( )( )2

=1

N[E1 s HH

0 t1( ),sVV

0 t1( ), s,er1( ) + E2 s HH

0 t2( ),sVV

0 t2( ), s,er2( ) + ...

+EN sHH

0 tN( ),sVV

0 tN( ), s,erN( )]


Monte-Carlo simulation

• The radar measurement noise

(0.7dB, 17%) is modeled by a

Gaussian random process.

• Errors in roughness estimate

is smaller than 10%.

• Real part of the dielectric

constant (εr) is retrieved first

and Mv error is smaller than

0.06 cm3/cm3.

Time-series search of lookup table

Snap-shot search of lookup table

• A snapshot search of the

same lookup table has no

constraint on roughness, is

subject to the ambiguity, and

the rmse is very large.


Validation with in situ data

• Truck-mounted radar measurements in

Ypsilanti, Michigan were obtained over

a two-month campaign (Oh et al. 2002).

• The LUT time-series and snap-shot

performs comparably most likely

because the radar measurement error

(~0.4dB) is smaller than 0.7dB.

• Dubois method has outliers.


Validation with in situ data

• The retrievals from all 4 sites are

combined in one scatter plot.

• Many retrievals of the Dubois retrieval

become outliers.

• Overall the LUT time-series retrieval

shows the best correlation with the in

situ mv and the best rmse in soil

moisture estimation.

LUT snapshot

0.0 0.1 0.2 0.3 0.4in situ (cm3/cm3)

0.0

0.1

0.2

0.3

0.4

retr

iev

al (

cm3/c

m3) rmse=0.055

mean_e=0.006

corr=0.82

LUT time-series

0.0 0.1 0.2 0.3 0.4in situ (cm3/cm3)

0.0

0.1

0.2

0.3

0.4

retr

iev

al (

cm3/c

m3) rmse=0.044

mean_e=0.013

corr=0.89

Dubois

0.0 0.1 0.2 0.3 0.4in situ (cm3/cm3)

0.0

0.1

0.2

0.3

0.4re

trie

val

(cm

3/c

m3) rmse > 1

mean_e > 1

corr= -0.14

Relative change index

0.0 0.1 0.2 0.3 0.4in situ (cm3/cm3)

0.0

0.2

0.4

0.6

0.8

1.0

ind

ex

corr=0.80


Effects of correlation length

• The validation with the Michigan data is performed: (a) uses l (correlation length) / s (rms height) of

10 (= the same as forward model). (b) uses the truth. The choice of l/s does not affect the Mv

retrieval.

Site (rms hgt) l/s =4 l/s = 7 l/s = 10 l/s = 15

1 (0.55cm) 0.037 0.041 0.038(a) 0.038(b)

2 (0.94cm) 0.043 0.048 (b) 0.051(a) 0.048

3 (1.78cm) 0.043(b) 0.043 0.047(a) 0.055

4 (3.47cm) 0.055(b) 0.042 0.040(a) 0.042

• Even if the value of the cost function changes, the

location of the minimum (=Mv retrieval) does not.

Retrieved Mv

• Change of l/s merely adds a bias to the cost function

+..


Effects of correlation length

l/s=15

l/s=4

• If a single scattering process is

dominant, the IEM shows that the

roughness effect and the dielectric

effect can be decoupled (Fung et

al. 1992; Shi et al. 1997):

σ0 (Mv, s, l/s) = f(Mv) + g(s, l/s)

Then

σ0 (Mv, s, l/s=a) - σ0 (Mv, s, l/s= b )

= g(s, l/s=a) - g(s, l/s=b)

= independent of Mv.

• The bias offset is uniform wrt

dielectric constant and

polarization.


Summary

• Findings

– Time-invariant roughness and soil moisture are estimated using the time-series method (2N inputs

solve N+1 unknowns).

– Does not require ancillary information.

– Simple search of a lookup table.

– Tested with in situ data: the error is 0.044 cm3/cm3 using 6-11 time-series inputs.

– The time-series method performs better than the other methods.

– Retrieval is mostly independent of the knowledge of correlation length one degree of freedom is

reduced.

• Discussion

– Increase in time-series window will further reduce the radar measurement noise improve

roughness estimate improve Mv retrieval.


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Soil moisture: retrieval performance

soil moisture retrieval.pptx

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